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A167031
a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.
5
1, 20, 337, 5461, 87653, 1403557, 22461349, 359399333, 5750460325, 92007649189, 1472123522981, 23553980911525, 376863712759717, 6029819476856741, 96477111920512933, 1543633791891427237, 24698140674915717029
OFFSET
0,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 16.
FORMULA
a(n) = (241*16^n - 65*4^n + 4)/180.
G.f.: (1-x+x^2)/((1-x)*(1-4*x)*(1-16*x)).
From G. C. Greubel, May 30 2016: (Start)
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-2).
E.g.f.: (1/180)*(241*exp(16*x) - 65*exp(4*x) + 4*exp(x)). (End)
MATHEMATICA
LinearRecurrence[{21, -84, 64}, {1, 20, 337}, 50] (* G. C. Greubel, May 30 2016 *)
PROG
(Magma) [ n le 2 select 19*n-18 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Oct 27 2009
STATUS
approved